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Table of Content

      
    20 December 2022
    Volume 57 Issue 12
    Community discovery algorithm based on label attention mechanism
    WANG Jing-hong, LIANG Li-na, LI Hao-kang, WANG Xi-zhao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  1-12.  doi:10.6040/j.issn.1671-9352.7.2021.097
    Abstract ( 418 )   PDF (7658KB) ( 192 )   Save
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    For network clustering, this paper proposes a community discovery algorithm based on label attention mechanism. Network features are jointly measured by label node frequency and inverse example node frequency, and attention mechanism is introduced to handle network features in order to make the metric of network features more focused on the detailed information of example nodes. Community division is composed of three parts: complex network preprocessing, network node strategy, and community game merging. The network nodes strategy is consists of three steps: the non-contributing node merging, the judgment of the node to the community and the judgment of the degree of the node. The experiments are verified with the help of real networks. The results show that the community discovery algorithm based on label attention mechanism outperforms other community discovery algorithms in four aspects: normalized mutual information, modularity, number of community divisions and running time. Applying this algorithm in real life can more intuitively show the existing connections within the network.
    Feature selection using adaptive neighborhood mutual information and spectral clustering
    SUN Lin, LIANG Na, XU Jiu-cheng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  13-24.  doi:10.6040/j.issn.1671-9352.7.2021.168
    Abstract ( 466 )   PDF (1214KB) ( 227 )   Save
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    In order to deal with the problem that traditional spectral clustering algorithms need set parameters manually, this paper proposes a feature selection algorithm based on adaptive neighborhood mutual information and spectral clustering, which takes the advantage of neighborhood rough sets to deal with continuous data. First, the standard deviation set and adaptive neighborhood set of each object on attribute are defined. Some uncertainty measures such as adaptive neighborhood entropy, average neighborhood entropy, joint entropy, neighborhood conditional entropy and neighborhood mutual information are given, and then the adaptive neighborhood mutual information is used to sort the correlation between features and labels. Second, the shared nearest neighbor spectral clustering algorithm is combined to cluster the strongly relevant features into the same feature cluster, so that the features in the different feature clusters are strongly diverse. Finally, the feature selection algorithm is designed by employing the minimum redundancy and maximum correlation technology. The experimental results of selecting the number of features and classification accuracy on ten datasets verify the effectiveness of the proposed algorithm.
    Transcendental solutions of two types of systems of complex differential-difference equations
    YANG Qi
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  25-33.  doi:10.6040/j.issn.1671-9352.0.2021.226
    Abstract ( 347 )   PDF (463KB) ( 209 )   Save
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    By the theory of complex differential equations and complex difference equations,this paper studies transcendental entire solutions with finite order of two types of systems of complex differential-difference equations, and obtains two results.
    Entire solutions of two types of nonlinear differential-difference equations
    GAO Zhen-guang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  34-44.  doi:10.6040/j.issn.1671-9352.0.2021.785
    Abstract ( 343 )   PDF (436KB) ( 367 )   Save
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    Using Nevanlinna's value distribution theory, this paper investigates the existence of entire solutions with finite order of two types of nonlinear differential-difference equations of the forms f n+ωf n-1f '+b(f ')n+qeQf(z+c)=uev and f n1f n-1f '+ω2(f ')n+qeQf(z+c)=p1eλ1z+p2eλ2z, and obtains two results. Examples are provided to show that the results obtained in this paper, in a sense, are best possible.
    Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces
    SHI Peng-wei, TAO Shuang-ping
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  45-54.  doi:10.6040/j.issn.1671-9352.0.2021.685
    Abstract ( 543 )   PDF (477KB) ( 208 )   Save
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    With the help of the boundedness of the Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of the parameterized Marcinkiewicz integral, the area integral and Littlewood-Paley g*λ function with rough kernel is obtained on grand variable Herz spaces. Meanwhile, the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g*λ function is also proved on grand variable Herz spaces.
    Boundedness of commutators for the Marcinkiewicz integral operators on Herz Triebel-Lizorkin spaces with variable exponent
    WEI Ying-ying, ZHANG Jing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  55-63.  doi:10.6040/j.issn.1671-9352.0.2021.656
    Abstract ( 427 )   PDF (473KB) ( 191 )   Save
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    An equivalent characterization of the norm for Herz Triebel-Lizorkin spaces with variable exponent is established by means of two operator families, Peetre maximal functions and the boundedness of Hardy-Littlewood maximal operators on vector-valued function spaces. Based on the result, the boundedness of commutators for the Marcinkiewicz integral operators on Herz Triebel-Lizorkin spaces with variable exponent is proved.
    Linear operators preserving transitive closures of matrices over the binary Boolean semiring
    DENG Wei-na, ZHAO Xian-zhong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  64-70.  doi:10.6040/j.issn.1671-9352.0.2022.044
    Abstract ( 392 )   PDF (405KB) ( 147 )   Save
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    The linear operators which preserve transitive closures of matrices over the binary Boolean semiring are studied, the characterizations of invertible linear operators which preserve transitive closures of matrices are given, and it is shown that the strong preservers are invertible when the order of the matrices n≥2.
    First cohomology of W(2)with coefficients in Kac modules
    DING Ya-zhou, WANG Shu-juan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  71-74.  doi:10.6040/j.issn.1671-9352.0.2021.724
    Abstract ( 261 )   PDF (376KB) ( 284 )   Save
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    Over a field of characteristic p>2, the first cohomology of Witt-type Lie superalgebra W(2)with coefficients in two classes of Kac modules is determined. That the first cohomology spaces of W(2)with coefficients in K(2ξ2)and K(ξ12)are 1-dimensional and 0-dimensional respectively is showed.
    Irreducible representations of Ore extensions of enveloping algebra of two-dimensional non-abelian Lie algebra
    LI Shi-yu, CHEN Chen, CHEN Hui-xiang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  75-80.  doi:10.6040/j.issn.1671-9352.0.2021.807
    Abstract ( 342 )   PDF (435KB) ( 132 )   Save
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    The irreducible representations of three classes of Hopf-Ore extensions of the enveloping algebra of 2-dimensional non-abelian Lie algebra over an algebraically closed field of characteristic zero are studied. The structures and isomorphism classifications of the finite dimensional simple modules over the three classes of Ore extensions are given respectively.
    Rank of the 1-singular transformation semigroup Tn(1)
    XU Bo, GAO Rong-hai, LU Lin-zhang, YOU Tai-jie
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  81-85.  doi:10.6040/j.issn.1671-9352.0.2022.126
    Abstract ( 317 )   PDF (404KB) ( 108 )   Save
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    Let n≥4, and Xn={1,2,…,n}. A new class of subsemigroups, 1-singular transformation semigroups of total transformation semigroups, is defined by non-singleton property, denoted by Tn(1). After determining the minimum generating set of the 1-singular transformation semigroup Tn(1)on Xn by idempotent analysis, it is proved that the rank of Tn(1)is n.
    Outer McCoy condition for modules
    LI Mei, CHENG Zhi
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  86-91.  doi:10.6040/j.issn.1671-9352.0.2021.789
    Abstract ( 287 )   PDF (370KB) ( 107 )   Save
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    The notion of outer McCoy modules and linearly outer McCoy modules are introduced. Some properties of outer McCoy modules are established, and an example is given to show that a left McCoy module may not be a right outer McCoy module. A necessary and sufficient condition for outer McCoy modules over standardly graded algebras is also established.
    On feckly-reduced rings
    WU Wen-tao, WANG Yao, REN Yan-li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  92-95.  doi:10.6040/j.issn.1671-9352.0.2021.658
    Abstract ( 342 )   PDF (371KB) ( 150 )   Save
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    We give some equivalent characterizations of feckly-reduced rings, and study the relationships between feckly-reduced rings and related rings.
    Zeroth-order general Randic index of quasi-tree graphs
    SUN Xiao-ling, GAO Yu-bin, DU Jian-wei, REN Jian-bin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  96-102.  doi:10.6040/j.issn.1671-9352.0.2021.184
    Abstract ( 377 )   PDF (516KB) ( 169 )   Save
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    By using the properties of the zeroth-order general Randic index and analyzing the structure of the quasi-tree graphs, the extremal values of zeroth-order general Randic indices of quasi-tree graphs with perfect matchings and p pendant vertices are determined. Furthermore, the corresponding extremal quasi-tree graphs are identified.
    k-Path vertex cover in Cartesian product graphs
    SUO Meng-ge, CHEN Jing-rong, ZHANG Juan-min
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(12):  103-110.  doi:10.6040/j.issn.1671-9352.0.2021.784
    Abstract ( 377 )   PDF (1148KB) ( 104 )   Save
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    For a graph G and a positive integer k, a subset S⊆V(G)is called a k-path vertex cover if any path of order k in G contains at least one vertex from S. The cardinality of the minimum k-path vertex cover is called the k-path vertex cover number of graph G, denoted by ψk(G). The k-path vertex cover problem of Cartesian product graphs in cycle graph and cycle graph, cycle graph and complete graph, cycle graph and complete bipartite graph is studied, and the exact value, upper or lower bound of ψk(G)is obtained.